Size Dependence of $L_{2,3}$ Branching Ratio and $2p$ Core-Hole Screening in X-Ray Absorption of Metal Clusters

Resonant $2p$ x-ray absorption spectra of size-selected transition metal ions and clusters consisting of $1\le n\le 200$ atoms are reported. Remnants of atomic multiplet splitting in $L_{2,3}$-edge x-ray absorption can be resolved up to the trimer, above which the overall line shape is already bulklike. A strong cluster size dependence of the $L_{2,3}$ branching ratio was found for titanium, vanadium, and cobalt clusters. While $3d$ electron delocalization increases with cluster size, the apparent $2p$ spin-orbit splitting remains constant within the error bars. The size dependence of the $L_{2,3}$ branching ratio can be attributed to cluster size specific screening of the $2p–3d$ Coulomb interaction by $3d/4s$ valence electrons.

Figure 1

$L_{2,3}$ x-ray absorption spectra of size-selected titanium clusters, measured at a photon energy resolution of 125 meV, compared to bulk titanium [5]. Already for the tetramer, the line shape is bulklike. There is good agreement of the monomer spectrum with the neutral atom [13] and calculations using the Cowan code [20] (stick spectrum and dotted line).

Figure 2

$L_{2,3}$ branching ratio of size-selected cobalt, vanadium, and titanium cluster ions (squares) and neutral clusters with a typical mass-resolution of five atoms (circles). For all clusters, intensity is transferred from the $L_3$ to the $L_2$ line with increasing cluster size. Bulk values are taken from [5, 22]. The dashed line is a guide to the eye. For titanium, data evaluated from the peak areas (triangles) are given for comparison.

Figure 3

$L_3$ x-ray absorption onset of free cobalt, vanadium, and titanium clusters (circles and squares as in Fig. 2). For vanadium and cobalt, the onsets shifts by $\approx 3\mathrm{eV}$ from monomer to bulk [5, 22]; this shift is smaller for titanium. The dashed line is a guide to the eye.

Figure 4

Apparent $2p$ spin-orbit splitting of free cobalt, vanadium, and titanium clusters (circles and squares as in Fig. 2). For all clusters up to the bulk [5, 22], the apparent $2p$ spin-orbit splitting is constant within the error bars. The dashed line gives the average value.